Modular Symmetries, Threshold Corrections And Moduli For $Z_2 \times Z_2 $ Orbifolds

TL;DR

This paper investigates the structure of ${Z}_2 imes {Z}_2$ orbifolds, deriving string loop threshold corrections, analyzing modular symmetries, and studying the effects of Wilson lines on moduli stabilization.

Contribution

It introduces a novel analysis of fixed planes in ${Z}_2 imes {Z}_2$ orbifolds and computes threshold corrections with symmetry groups as subgroups of $PSL(2,Z)$.

Findings

Threshold corrections exhibit subgroup symmetries of $PSL(2,Z)$.

Effective potential for gaugino condensate is constructed and minimized.

Wilson lines influence the modular symmetry structure.

Abstract

${\bf Z}_2\times {\bf Z}_2$ Coxeter orbifolds are constructed with the property that some twisted sectors have fixed planes for which the six-torus can not be decomposed into a direct sum ${\bf T}^2\bigoplus{\bf T}^4 $ with the fixed plane lying in ${\bf T}^2$. The string loop threshold corrections to the gauge coupling constants are derived, and display symmetry groups for the $T$ and $U$ moduli that are subgroups of the full modular group $PSL(2,Z)$. The effective potential for duality invariant gaugino condensate in the presence of hidden sector matter is constructed and minimized for the values of the moduli. The effect of Wilson lines on the modular symmetries is also studied.